Research related to user authentication techniques in vehicular ad hoc networks (VANETs) has received significant attention in the last decade. However, its security and privacy still become a central issue that is widely open to discussion. In 2016, Vijayakumar {\it et al.} published dual authentication and key management techniques for secure data transmission in VANETs. The dual authentication scheme aims to provide high security on the vehicle side to prevent unauthorized vehicles from entering the VANETs effectively. The authentication process relies on the fingerprint and hash code ($HC$). The authors claimed the mechanism could withstand the replaying attack by appending it with an updated timestamp and the packet's transmission. However, this paper shows that their scheme suffered a denial of service (DoS) attack due to misplaced timestamps. So, we propose an improvement of their scheme to withstand the attacks.